In this thesis we study the problem of robotic interaction with objects from a flexible perspective that complements the rigid force-closure approach. In a flexible interaction the object is not firmly bound to the robot (immobilized), which leads to many interesting scenarios. We focus on the secure kind of flexible interactions, commonly referred to as caging grasps. In this context, the adjective secure implies that the object is not able to escape arbitrarily far away from the robot which is caging it. A cage is a secure flexible interaction because it does not immobilize the object, but restricts its motion to a finite set of possible configurations. We study cages in two novel scenarios for objects with holes: caging through multi-agent cooperation and through dual-arm knotting with a rope. From these two case studies, we were able to analyze the caging problem in a broader perspective leading to the definition of a hierarchical classification of flexible interactions and cages.

In parallel to the geometric and physical problem of flexible interactions with objects, we study also the problem of discrete action scheduling through a novel control architecture called Behavior Trees (BTs). In this thesis we propose a formulation that unifies the competing BT philosophies into a single framework. We analyze how the mainstream BT formulations differ from each other, as well as their benefits and limitations. We also compare the plan representation capabilities of BTs with respect to the traditional approach of Controlled Hybrid Dynamical Systems (CHDSs). In this regard, we present bidirectional translation algorithms between such representations as well as the necessary and sufficient conditions for translation convergence. Lastly, we demonstrate our action scheduling BT architecture showcasing the aforementioned caging scenarios, as well as other examples that show how BTs can be interfaced with other high level planners.